Why can I look at a graph and immediately find the closest point to another point, but it takes me O(n) time through programming?

Let me clarify: Given a scatterplot of some given number of points n, if I want to find the closest point to any point in the plot mentally, I can immediately ignore most points in the graph, narrowing my choices down to some small, constant number of points nearby. Yet, in programming, given a set of points n, in order to find the closest point to any one, it requires checking every other point, which is ${\cal O}(n)$ time. I am guessing that the visual sight of a graph is likely the equivalent of some data structure I am incapable of understanding; because with programming, by converting the points to a more structured method such as a quadtree, one can find the closest points to $k$ points in $n$ in $k\cdot\log(n)$ time, or ammortized ${\cal O}(\log n)$ time. But there is still no known ${\cal O}(1)$ ammortized algorithms (that I can find) for point-finding after data restructuring. So why does this appear to be possible with mere visual inspection?